Note

You can download this demonstration as a Jupyter Notebook
`here`

# Button network¶

This notebook presents an agent-based model of randomly connecting buttons. It demonstrates how to use the agentpy package to work with networks and visualize averaged time-series for discrete parameter samples.

```
[1]:
```

```
# Model design
import agentpy as ap
import networkx as nx
import random
# Visualization
import seaborn as sns
```

## About the model¶

This model is based on the Agentbase Button model by Wybo Wiersma and the following analogy from Stuart Kauffman:

“Suppose you take 10,000 buttons and spread them out on a hardwood floor. You have a large spool of red thread. Now, what you do is you pick up a random pair of buttons and you tie them together with a piece of red thread. Put them down and pick up another random pair of buttons and tie them together with a red thread, and you just keep doing this. Every now and then lift up a button and see how many buttons you’ve lifted with your first button. A connective cluster of buttons is called a cluster or a component. When you have 10,000 buttons and only a few threads that tie them together, most of the times you’d pick up a button you’ll pick up a single button.

As the ratio of threads to buttons increases, you’re going to start to get larger clusters, three or four buttons tied together; then larger and larger clusters. At some point, you will have a number of intermediate clusters, and when you add a few more threads, you’ll have linked up the intermediate-sized clusters into one giant cluster.

So that if you plot on an axis, the ratio of threads to buttons: 10,000 buttons and no threads; 10,000 buttons and 5,000 threads; and so on, you’ll get a curve that is flat, and then all of a sudden it shoots up when you get this giant cluster. This steep curve is in fact evidence of a phase transition.

If there were an infinite number of threads and an infinite number of buttons and one just tuned the ratios, this would be a step function; it would come up in a sudden jump. So it’s a phase transition like ice freezing.

Now, the image you should take away from this is if you connect enough buttons all of a sudden they all go connected. To think about the origin of life, we have to think about the same thing.”

## Model definition¶

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```
# Define the model
class ButtonModel(ap.Model):
def setup(self):
# Create a graph with n agents
self.buttons = self.add_network()
self.buttons.add_agents(self.p.n)
self.threads = 0
def update(self):
# Record size of the biggest cluster
clusters = nx.connected_components(self.buttons.graph)
max_cluster_size = max([len(g) for g in clusters]) / self.p.n
self.record('max_cluster_size', max_cluster_size)
# Record threads to button ratio
self.record('threads_to_button', self.threads / self.p.n)
def step(self):
# Create random edges based on parameters
for _ in range(int(self.p.n * self.p.speed)):
self.buttons.graph.add_edge(*self.agents.random(2))
self.threads += 1
```

## Multi-run experiment¶

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```

```
# Define parameter ranges
parameter_ranges = {
'steps': 30, # Number of simulation steps
'speed': 0.05, # Speed of connections per step
'n': (100, 1000, 10000) # Number of agents
}
# Create sample for different values of n
sample = ap.sample_discrete(parameter_ranges)
# Keep dynamic variables
exp = ap.Experiment(ButtonModel, sample, iterations=25, record=True)
# Perform 75 seperate simulations (3 parameter combinations * 25 repetitions)
results = exp.run()
```

```
Scheduled runs: 75
Completed: 75, estimated time remaining: 0:00:00
Experiment finished
Run time: 0:00:59.906876
```

```
[4]:
```

```
# Plot averaged time-series for discrete parameter samples
sns.set()
data = results.arrange_variables()
ax = sns.lineplot(data=data, x='threads_to_button', y='max_cluster_size', hue='n')
```